A bank contains pennies, nickels, dimes, quarters and half-dollars. How many different sets of three coins can be formed?
(PS. As the answer is given to be 35, it is assumed that 7 coins are present in the bank.)
The problem does not specify the total number of coins. If the total number of pennies, nickels, dimes, quarters and half-dollars in the bank is equal to n, the number of sets of three coins that can be formed is given by C(n, r) = `(n!)/(r!*(n-r)!)`
If the total number of coins in the bank is 7, C(7,3) = `(7!)/(3!*(7-3)!) ` = `(7*6*5*4)/(4*3*2*1)` = 35
The total number of sets of 3 coins that can be formed given 7 coins in all is 35.